Finite Group Databasebeta

← C2×#10593941 #11903261

Subgroups — C2×#10593941 #11903261

Order 1152.

2549 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#634C211yesmaximal, characteristic, complemented
2C2×C3×C4×D12C211yesmaximal, characteristic
3C2×C3×#870C211yesmaximal, characteristic, complemented
4C2×#63919C211yesmaximal, characteristic, complemented
5C2×#63898C211yesmaximal, characteristic
6C2×#63898C211yesmaximal, characteristic
7C2×#63896C212yesmaximal, complemented
8C2×#63893C212yesmaximal, complemented
9C2×D3×Dic3⋊C4C212yesmaximal, complemented
10C2×#63872C211yesmaximal, characteristic, complemented
11C2×#63851C212yesmaximal, complemented
12#10593941C2116yesmaximal, direct product factor
13C2×#5690—31nomaximal
14C2×#5539—31nomaximal
15C22×#634C2211yescharacteristic
16C22×C3×D12C2211yescharacteristic
17C22×C3×C4×D3C2212yes—
18C22×#627C2212yes—
19C22×D3×Dic3C2212yes—
20C22×D3×Dic3C2212yes—
21C2×C32×C42C2211yescharacteristic
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×C4×C3⋊Dic3C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C4×#634C2218yescomplemented
28C2×C3×(C2×D3)⋊C4C2212yes—
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×Dic3⋊C4C2212yes—
33C2×C3×Dic3⋊C4C2212yes—
34C3×C4×D12C2218yes—
35C3×#870C2218yescomplemented
36C2×#3724C2212yes—
37C2×Dic3⋊Dic3C2212yes—
38C2×Dic3⋊Dic3C2212yes—
39C2×(C2×D3)⋊Dic3C2212yes—
40C2×(C2×D3)⋊Dic3C2212yes—
41#63919C2218yescomplemented
42#63898C2218yes—
43#63898C2218yes—
44#63896C22116yescomplemented
45#63893C22116yescomplemented
46D3×Dic3⋊C4C22116yescomplemented
47#63872C2218yescomplemented
48#63851C22116yescomplemented
49C2×C3×#125—31no—
50C2×C3×C4×D4—31no—
51C2×D4×Dic3—31no—
52C2×D4×Dic3—31no—
53C2×#924—32no—
54C22×Dic3⋊C4—32no—
55#5690—316no—
56#5539—316no—
57C2×#897—32no—
58C2×#896—32no—
59C2×#896—32no—
60C2×#893—31no—
61C2×#893—31no—
62C2×D3×C4⋊C4—32no—
63C2×#890—31no—
64C2×#890—31no—
65C2×#888—31no—
66C2×#888—31no—
67C2×#878—32no—
68C2×#878—32no—
69C2×C4×D12D311yescharacteristic
70C2×#870D311yescharacteristic, complemented
71C2×C4×Dic6—31no—
72C2×C4×Dic6—31no—
73C2×C4×Dic6—61no—
74C23×C3×D3C2312yes—
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C2×#634—24no—
83C2×#634C2314yes—
84C22×C3×Dic3C2312yes—
85C22×C3×Dic3C2312yes—
86C22×C3×Dic3C2312yes—
87C2×C3×D12Q818yescomplemented
88C2×C3×D12C2314yes—
89C2×C3×C4×D3—44no—
90C2×C3×C4×D3C2318yes—
91C2×#627—44no—
92C2×#627C2318yes—
93C2×D3×Dic3—28no—
94C2×D3×Dic3—44no—
95C2×D3×Dic3C2318yes—
96C2×D3×Dic3C2318yes—
97C32×C42C2314yes—
98C4⋊(C3⋊Dic3)C2314yes—
99#3750C2314yes—
100#3750C2314yes—
101C4×C3⋊Dic3C2314yes—
102C4×C3⋊Dic3C2314yes—
103C3×(C2×D3)⋊C4C2318yes—
104C3×C4⋊Dic3C2314yes—
105C3×C4⋊Dic3C2314yes—
106C3×C4⋊Dic3C2314yes—
107C3×Dic3⋊C4C2318yes—
108C3×Dic3⋊C4C2318yes—
109#3724C2318yes—
110Dic3⋊Dic3C2318yes—
111Dic3⋊Dic3C2318yes—
112(C2×D3)⋊Dic3C2318yes—
113(C2×D3)⋊Dic3C2318yes—
114C2×#554—91noSylow
115C22×C3×D4—31no—
116C23×C3×C4—32no—
117C23×Dic3—32no—
118C23×Dic3—32no—
119C22×D12C2×D311yescharacteristic
120C22×C4×D3—32no—
121C22×C4×D3—32no—
122C22×C4×D3C2×D312yes—
123C22×Dic6—31no—
124C22×Dic6—31no—
125C22×Dic6—32no—
126C22×Dic6—32no—
127C22×Dic6—61no—
128C3×#125—38no—
129C3×C4×D4—38no—
130C2×C3×C4⋊C4—32no—
131C2×C3×C4⋊C4—32no—
132C2×C3×C4⋊C4—31no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C22⋊C4—32no—
136C2×C3×C42—21no—
137C2×C3×C42C2×D311yescharacteristic
138C2×C3×C42C2×D311yescharacteristic
139C2×#217—32no—
140C2×#217—32no—
141D4×Dic3—38no—
142D4×Dic3—38no—
143C2×(C2×D3)⋊C4—32no—
144C2×(C2×D3)⋊C4—32no—
145C2×(C2×D3)⋊C4C2×D312yes—
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3—32no—
149C2×C4⋊Dic3—32no—
150C2×C4⋊Dic3—61no—
151C2×C4⋊Dic3C2×D311yescharacteristic
152C2×C4⋊Dic3C2×D311yescharacteristic
153C2×C4⋊Dic3C2×D311yescharacteristic
154#924—316no—
155C2×Dic3⋊C4—31no—
156C2×Dic3⋊C4—31no—
157C2×Dic3⋊C4—31no—
158C2×Dic3⋊C4—31no—
159C2×Dic3⋊C4—32no—
160C2×Dic3⋊C4—32no—
161C2×Dic3⋊C4—32no—
162C2×Dic3⋊C4—32no—
163C2×Dic3⋊C4—316no—
164C2×Dic3⋊C4—61no—
165C2×Dic3⋊C4—61no—
166C2×Dic3⋊C4C2×D312yes—
167C2×Dic3⋊C4C2×D312yes—
168C2×C4×Dic3—31no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—61no—
173C2×C4×Dic3—61no—
174#897—316no—
175#896—316no—
176#896—316no—
177#893—38no—
178#893—38no—
179D3×C4⋊C4—316no—
180#890—38no—
181#890—38no—
182#888—38no—
183#888—38no—
184#878—316no—
185#878—316no—
186C4×D12C2×D318yes—
187#870C2×D318yescomplemented
188C4×Dic6—38no—
189C4×Dic6—38no—
190C4×Dic6—68no—
191C23×C32C2411yescharacteristic
192C22×C3×D3—24no—
193C22×C3×D3—24no—
194C22×C3×D3C2×Q818yes—
195C22×C3×D3C2414yes—
196C2×C32×C4—22no—
197C2×C32×C4—22no—
198C2×C32×C4C2×Q814yes—
199C2×C32×C4C2412yes—
200C2×C32×C4C2412yes—
201C2×C32×C4C2412yes—
202C2×C3⋊Dic3—22no—
203C2×C3⋊Dic3—22no—
204C2×C3⋊Dic3—22no—
205C2×C3⋊Dic3#4114yes—
206C2×C3⋊Dic3C2412yes—
207C2×C3⋊Dic3C2412yes—
208C2×C3⋊Dic3C2412yes—
209C2×C3⋊Dic3C2412yes—
210#634—28no—
211C2×C3×Dic3—24no—
212C2×C3×Dic3—24no—
213C2×C3×Dic3—24no—
214C2×C3×Dic3C2414yes—
215C2×C3×Dic3C2414yes—
216C2×C3×Dic3C2414yes—
217C3×D12C2×Q8116yescomplemented
218C3×C4×D3—48no—
219#627—48no—
220D3×Dic3—216no—
221D3×Dic3—48no—
222#554—916no—
223C2×C4⋊Q8—91no—
224C2×#125—31no—
225C2×#125—91no—
226C2×C22⋊Q8—92no—
227C2×C22⋊Q8—92no—
228C2×C22⋊Q8—92no—
229C2×C4×Q8—91no—
230C2×C4×D4—31no—
231C2×C4×D4—91no—
232C2×C4×D4—91no—
233C22×C4⋊C4—92no—
234C24×C3—32no—
235C23×D3C22×D312yes—
236C2×C3×D4—38no—
237C2×C3×D4—34no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—21no—
241C22×C3×C4—32no—
242C22×C3×C4—32no—
243C22×C3×C4—32no—
244C22×C3×C4—38no—
245C22×C3×C4—124no—
246C22×C3×C4C22×D311yescharacteristic
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C22×Dic3—31no—
253C22×Dic3—31no—
254C22×Dic3—31no—
255C22×Dic3—31no—
256C22×Dic3—31no—
257C22×Dic3—31no—
258C22×Dic3—31no—
259C22×Dic3—31no—
260C22×Dic3—38no—
261C22×Dic3—38no—
262C22×Dic3—61no—
263C22×Dic3—61no—
264C22×Dic3—61no—
265C22×Dic3—61no—
266C22×Dic3—68no—
267C22×Dic3—124no—
268C22×Dic3C22×D312yes—
269C22×Dic3C22×D312yes—
270C22×Dic3C22×D312yes—
271C2×D12Dic618yescomplemented
272C2×D12C22×D314yes—
273C2×C4×D3—38no—
274C2×C4×D3—38no—
275C2×C4×D3—44no—
276C2×C4×D3—68no—
277C2×C4×D3—124no—
278C2×C4×D3C22×D318yes—
279C2×Dic6—34no—
280C2×Dic6—34no—
281C2×Dic6—38no—
282C2×Dic6—38no—
283C2×Dic6—64no—
284C2×Dic6—64no—
285C2×Dic6—64no—
286C2×Dic6—68no—
287C2×Dic6—124no—
288C2×Dic6—124no—
289C3×C4⋊C4—34no—
290C3×C4⋊C4—34no—
291C3×C4⋊C4—34no—
292C3×C4⋊C4—38no—
293C3×C4⋊C4—38no—
294C3×C22⋊C4—38no—
295C3×C42—24no—
296C3×C42C22×D314yes—
297C3×C42C22×D314yes—
298#217—38no—
299#217—38no—
300(C2×D3)⋊C4—38no—
301(C2×D3)⋊C4—38no—
302(C2×D3)⋊C4C22×D318yes—
303C4⋊Dic3—34no—
304C4⋊Dic3—34no—
305C4⋊Dic3—38no—
306C4⋊Dic3—38no—
307C4⋊Dic3—64no—
308C4⋊Dic3C22×D314yes—
309C4⋊Dic3C22×D314yes—
310C4⋊Dic3C22×D314yes—
311Dic3⋊C4—34no—
312Dic3⋊C4—34no—
313Dic3⋊C4—34no—
314Dic3⋊C4—34no—
315Dic3⋊C4—38no—
316Dic3⋊C4—38no—
317Dic3⋊C4—38no—
318Dic3⋊C4—38no—
319Dic3⋊C4—64no—
320Dic3⋊C4—64no—
321Dic3⋊C4C22×D318yes—
322Dic3⋊C4C22×D318yes—
323C4×Dic3—34no—
324C4×Dic3—34no—
325C4×Dic3—34no—
326C4×Dic3—34no—
327C4×Dic3—64no—
328C4×Dic3—64no—
329C22×C32C22×Q812yes—
330C22×C32C2×#4112yes—
331C22×C32H(5,𝔽2)12yes—
332C22×C32C2511yescharacteristic
333C2×C3×D3—216no—
334C2×C3×D3—24no—
335C2×C3×D3—24no—
336C2×C3×D3C22×Q818yes—
337C32×C4—22no—
338C32×C4—22no—
339C32×C4C22×Q814yes—
340C3⋊Dic3—22no—
341C3⋊Dic3—22no—
342C3⋊Dic3—22no—
343C3⋊Dic3C2×#4114yes—
344C3×Dic3—24no—
345C3×Dic3—24no—
346C3×Dic3—24no—
347C22×Q8—92no—
348C22×Q8—91no—
349C22×D4—31no—
350C23×C4—32no—
351C23×C4—92no—
352C23×C4—92no—
353C4⋊Q8—98no—
354#125—38no—
355#125—98no—
356C22⋊Q8—916no—
357C22⋊Q8—916no—
358C22⋊Q8—916no—
359C4×Q8—98no—
360C4×D4—38no—
361C4×D4—98no—
362C4×D4—98no—
363C2×C4⋊C4—32no—
364C2×C4⋊C4—31no—
365C2×C4⋊C4—31no—
366C2×C4⋊C4—31no—
367C2×C4⋊C4—32no—
368C2×C4⋊C4—916no—
369C2×C4⋊C4—92no—
370C2×C4⋊C4—92no—
371C2×C4⋊C4—92no—
372C2×C4⋊C4—91no—
373C2×C4⋊C4—91no—
374C2×C4⋊C4—91no—
375C2×C22⋊C4—32no—
376C2×C22⋊C4—92no—
377C2×C22⋊C4—92no—
378C2×C42—91no—
379C2×C42—91no—
380C2×C42D3211yescharacteristic
381C23×C3—21no—
382C23×C3—38no—
383C23×C3—34no—
384C23×C3—64no—
385C23×C3—64no—
386C23×C3C23×D311yescharacteristic
387C23×C3C23×D311yescharacteristic
388C22×D3—24no—
389C22×D3—24no—
390C22×D3C2×Dic618yes—
391C22×D3C23×D314yes—
392C3×D4—316no—
393C2×C3×C4—24no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—24no—
402C2×C3×C4—34no—
403C2×C3×C4—34no—
404C2×C3×C4—34no—
405C2×C3×C4—42no—
406C2×C3×C4—64no—
407C2×C3×C4—64no—
408C2×C3×C4—64no—
409C2×C3×C4—128no—
410C2×C3×C4C2×Dic614yes—
411C2×C3×C4D3×Q814yes—
412C2×C3×C4C23×D312yes—
413C2×C3×C4C23×D312yes—
414C2×C3×C4C23×D312yes—
415C2×C3×C4C23×D312yes—
416C2×C3×C4C23×D312yes—
417C2×C3×C4C23×D312yes—
418C2×Dic3—24no—
419C2×Dic3—24no—
420C2×Dic3—24no—
421C2×Dic3—34no—
422C2×Dic3—34no—
423C2×Dic3—32no—
424C2×Dic3—32no—
425C2×Dic3—32no—
426C2×Dic3—32no—
427C2×Dic3—32no—
428C2×Dic3—32no—
429C2×Dic3—32no—
430C2×Dic3—32no—
431C2×Dic3—64no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—62no—
436C2×Dic3—616no—
437C2×Dic3—64no—
438C2×Dic3—62no—
439C2×Dic3—62no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442C2×Dic3—62no—
443C2×Dic3—62no—
444C2×Dic3—122no—
445C2×Dic3—122no—
446C2×Dic3—128no—
447C2×Dic3C23×D314yes—
448C2×Dic3C23×D314yes—
449C2×Dic3C23×D314yes—
450D12C2×Dic6116yescomplemented
451C4×D3—48no—
452C4×D3—616no—
453C4×D3—128no—
454Dic6—68no—
455Dic6—68no—
456Dic6—616no—
457Dic6—128no—
458Dic6—128no—
459C2×C32#55414yescomplemented
460C2×C32C23×Q811yescharacteristic
461C2×C32C22×#4111yescharacteristic
462C2×C32C2×H(5,𝔽2)11yescharacteristic
463C3×D3—28no—
464C24—32no—
465C2×Q8—98no—
466C2×Q8—94no—
467C2×Q8—184no—
468C2×Q8—364no—
469C2×D4—34no—
470C2×D4—38no—
471C22×C4—32no—
472C22×C4—32no—
473C22×C4—32no—
474C22×C4—38no—
475C22×C4—98no—
476C22×C4—98no—
477C22×C4—91no—
478C22×C4—91no—
479C22×C4—91no—
480C22×C4—91no—
481C22×C4—124no—
482C22×C4—188no—
483C22×C4—364no—
484C22×C4C2×D3211yescharacteristic
485C22×C4C2×D3211yescharacteristic
486C22×C4C2×D3211yescharacteristic
487C4⋊C4—38no—
488C4⋊C4—34no—
489C4⋊C4—34no—
490C4⋊C4—34no—
491C4⋊C4—38no—
492C4⋊C4—98no—
493C4⋊C4—98no—
494C4⋊C4—98no—
495C4⋊C4—94no—
496C4⋊C4—94no—
497C4⋊C4—94no—
498C22⋊C4—38no—
499C22⋊C4—98no—
500C22⋊C4—98no—
501C42—94no—
502C42—94no—
503C42C2×D3214yes—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—21no—
508C22×C3—38no—
509C22×C3—616no—
510C22×C3—64no—
511C22×C3—64no—
512C22×C3C22×Dic612yes—
513C22×C3#100412yes—
514C22×C3C2×D3×Q812yes—
515C22×C3D3×#4112yes—
516C22×C3D3×#4112yes—
517C22×C3#100912yes—
518C22×C3C24×D311yescharacteristic
519C22×C3C24×D311yescharacteristic
520C2×D3—24no—
521C2×D3—24no—
522C2×D3—216no—
523C2×D3C22×Dic618yes—
524C3×C4—24no—
525C3×C4—22no—
526C3×C4—22no—
527C3×C4—22no—
528C3×C4—22no—
529C3×C4—24no—
530C3×C4—42no—
531C3×C4—64no—
532C3×C4—64no—
533C3×C4—64no—
534C3×C4C22×Dic614yes—
535C3×C4C2×D3×Q814yes—
536Dic3—24no—
537Dic3—24no—
538Dic3—24no—
539Dic3—34no—
540Dic3—34no—
541Dic3—64no—
542Dic3—64no—
543Dic3—62no—
544Dic3—62no—
545Dic3—62no—
546Dic3—62no—
547Dic3—62no—
548Dic3—62no—
549Dic3—122no—
550Dic3—122no—
551C32C2×#55411yescharacteristic, complemented, Sylow
552C23—38no—
553C23—34no—
554C23—64no—
555C23—64no—
556C23C22×D3211yescharacteristic
557Q8—188no—
558Q8—368no—
559D4—316no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—34no—
563C2×C4—34no—
564C2×C4—34no—
565C2×C4—64no—
566C2×C4—64no—
567C2×C4—64no—
568C2×C4—94no—
569C2×C4—92no—
570C2×C4—92no—
571C2×C4—92no—
572C2×C4—92no—
573C2×C4—128no—
574C2×C4—1816no—
575C2×C4—182no—
576C2×C4—182no—
577C2×C4—182no—
578C2×C4—368no—
579C2×C4D3×Dic614yes—
580C2×C4C22×D3212yes—
581C2×C4C22×D3212yes—
582C2×C4C22×D3212yes—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—24no—
587C2×C3—68no—
588C2×C3#553914yescomplemented
589C2×C3#569014yescomplemented
590C2×C3C23×Dic611yescharacteristic
591C2×C3C2×#100411yescharacteristic
592C2×C3C22×D3×Q811yescharacteristic
593C2×C3C2×D3×#4111yescharacteristic
594C2×C3C2×D3×#4111yescharacteristic
595C2×C3C2×#100911yescharacteristic
596D3—28no—
597C22—38no—
598C22—64no—
599C22—64no—
600C22—616no—
601C22C2×D3×Dic612yes—
602C22#6430612yes—
603C22#6430712yes—
604C22C23×D3211yescharacteristic
605C4—22no—
606C4—22no—
607C4—64no—
608C4—64no—
609C4—64no—
610C4—94no—
611C4—182no—
612C4—182no—
613C4—182no—
614C4C2×D3×Dic614yes—
615C3—21no—
616C3C2×#553911yescharacteristic, complemented
617C3C2×#569011yescharacteristic, complemented
618C2—68no—
619C2#1059394114yesdirect product factor
620C2C22×D3×Dic611yescharacteristic
621C2C2×#6430611yescharacteristic
622C2C2×#6430711yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
prime radicalC22×C3×D12C22
hypercenterC2×C42D32
hypocenterC32C2×#554
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C4×#634C2semidirect
3. C2×C3×#870C2semidirect
4. C2×#63919C2semidirect
7. C2×#63896C2semidirect
8. C2×#63893C2semidirect
9. C2×D3×Dic3⋊C4C2semidirect
10. C2×#63872C2semidirect
11. C2×#63851C2semidirect
12. #10593941C2direct (N × H)
27. C4×#634C22semidirect
35. C3×#870C22semidirect
41. #63919C22semidirect
44. #63896C22semidirect
45. #63893C22semidirect
46. D3×Dic3⋊C4C22semidirect
47. #63872C22semidirect
48. #63851C22semidirect
70. C2×#870D3semidirect
87. C2×C3×D12Q8semidirect
187. #870C2×D3semidirect
217. C3×D12C2×Q8semidirect
271. C2×D12Dic6semidirect
450. D12C2×Dic6semidirect
459. C2×C32#554semidirect
551. C32C2×#554semidirect
588. C2×C3#5539semidirect
589. C2×C3#5690semidirect
616. C3C2×#5539semidirect
617. C3C2×#5690semidirect
619. C2#10593941direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C4×#6342
C2×C3×C4×D122
C2×C3×#8702
C2×#639192
C2×#638982
C2×#638962
C2×#638932
C2×D3×Dic3⋊C42
C2×#638722
C2×#638512
#105939412
C2×#56903
C2×#55393